6p(1/5)+9p(1/5)+9=12

Solution for 6p(1/5)+9p(1/5)+9=12 equation:

6p(1/5)+9p(1/5)+9=12

We move all terms to the left:

6p(1/5)+9p(1/5)+9-(12)=0

We add all the numbers together, and all the variables

6p(+1/5)+9p(+1/5)+9-12=0

We add all the numbers together, and all the variables

6p(+1/5)+9p(+1/5)-3=0

We multiply parentheses

6p^2+9p^2-3=0

We add all the numbers together, and all the variables

15p^2-3=0

a = 15; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·15·(-3)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*15}=\frac{0-6\sqrt{5}}{30}
=-\frac{6\sqrt{5}}{30}
=-\frac{\sqrt{5}}{5}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*15}=\frac{0+6\sqrt{5}}{30}
=\frac{6\sqrt{5}}{30}
=\frac{\sqrt{5}}{5}
$